You should look at this thread MacBook Pro loses access to 1 memory slot upon shutdown or reboot in OS X 10.8.1
I'm having the same issue with a Mid-2011 Mac Mini (purchased 2013). As in that linked tread, overheating after OS upgrade (in my case , Mavericks) seems to be related. I had constant crashes at sleep beginning about three weeks ago, and three tones at boot. For about two weeks I could get it to reboot by unplugging and giving it some time. Until today. Cleaned. Tested both chips in both possible slots, but will always get three tones when either chip is in top slot, fine when that slot is empty. Hardware test appears to just ignore an empty slot, so really not helpful (and won't boot with filled slot).
I'm not going to get into "loosening screws" as suggested in linked discussion, but that may work for a powerbook. It sounds like heat related warping. I saw early problems with this after 10.9.5 upgrade. Ended up building a special vertical stand (Mini's venting is rather poor) and installed "Temperature Monitor" by Marcel Bresink Software, which I recommend. This got the heat under control, but it looks like the damage was done. Now I'm running on 8gb memory, which dramatically shortens the life of the machine. It won't be a candidate for a Yosemite upgrade coming shortly.
Must say I'm pretty disappointed in "Apple quality". Had similar experience (repeated shorts of logic board, replaced 3 times) with a MacBook c.1997, when Apple Co. was looking like it might not survive, and lots of folks were having such problems. But at least then they would repair it for free. Given the premium price (without premium quality), I think this will be my last Mac, after having started with a Plus in the 1980s.